Overview

expoFitter is a specialized tool for visualizing and fitting non-linear electrophysiological data, built using R, Shiny, and Flexdashboard. The tool provides robust methodologies for fitting dynamic processes through single- and double-exponential models, allowing researchers to extract time constants and assess model fitness. Its robust non-linear least squares optimization makes expoFitter efficient for fitting complex data.

In scientific applications, expoFitter, or its backend logic, has been used to analyze slow neuronal currents like the calcium-dependent potassium current (\(I_{KCa}\); Ellison et al., in progress; Thuma et al., in progress). While it does not directly measure intracellular calcium (\([Ca^{2+}]_i\)) dynamics, the tool’s modeling logic and uncovered temporal information have served as indirect measures of \([Ca^{2+}]_i\) time-dependent changes in neurons of the lobster pyloric network, as demonstrated in ongoing research (Ellison et al., in progress; Thuma et al., in progress).

Tool Features

• Data Preprocessing and Filtering: Incorporates a unique data wrangling/filtering algorithm that utilizes both finite and simple differentiation to extract salient parts of the current trace, ensuring accurate and reliable model fits. This preprocessing step is essential for isolating active portions of the current.

• Native Model Parameter Approximator: Integrates approximator functionality automating model initial condition estimates based on quintessential features of the experimental data. Given the robustness of the optimizer, this reduces the need for manual adjustment of these parameters by the user.

• Flexible and Robust Exponential Model Fitting: Supports both single- and double-exponential model fits using the nlsLM algorithm from the minpack.lm package. The nlsLM algorithm implements the Levenberg-Marquardt Algorithm, which combines gradient descent and the Gauss-Newton method for robust non-linear least squares optimization (see Supplemental Information). The application fits experimental data using the following exponential models:

  • Single-Exponential Model:

  \[I = A e^{-\frac{t}{B}} + C\]

  • Double-Exponential Model:

  \[I = A e^{-\frac{t}{B}} + C e^{-\frac{t}{D}} + E\]

  where \(B\) and \(D\) represent the time constants of the first and second phase of the exponential curve, respectively.

• Interactive Visualization and Model Parameter Adjustment: Provides an interactive interface for data visualization and model fitting, enabling users to dynamically adjust model parameters through sliders and observe the resultant model solution both quantitatively and visually.

Installation

expoFitter Locally

There are several ways to access expoFitter. If you want the entirety of the repository, you can clone it to your local machine using these terminal commands (terminal used generically throughout):

git clone https://github.com/ryEllison/expoFitter.git
cd expoFitter

Ensure you are in the desired directory before executing the terminal commands. You can also use a point-and-click approach by navigating to Code in Github and selecting Download ZIP. Downloading expoFitter this way will require your moving expoFitter from your local downloads to the desired location on your machine before decompressing the file.

To run expoFitter locally, ensure that R is installed on your system, as well as the following packages:

• dplyr 1.1.4
• minpack.lm 1.2.4
• DT 0.33
• shiny 1.9.1

and your system’s environmental variables provide terminal access to R’s interpreter Rscript. Package installation is automated and can be completed by running the install_dependencies pseudo-executable in the \bin directory.

expoFitter can then be deployed utilizing your machine as a local server via the expoFitter_R pseudo-executable in the \bin directory. To make any tweaks or alterations to the tool to fit your particular use case, the code is dispersed throughout appropriate directories (e.g., \app, \scripts, and \src).

expoFitter as Electron App

expoFitter has also been built as a portable, desktop Electron app. The Electron build can be found in the \electron directory. However, for access to the desktop app the \installer directory can be downloaded using this terminal approach:

git clone --no-checkout https://github.com/ryEllison/expoFitter.git
cd expoFitter
git sparse-checkout init --cone
git sparse-checkout set ./installer
git checkout master
cd installer
pseudo_installer.bat

Again, ensuring you are in the directory where you wish the installer to be placed before executing the terminal commands.

You can also use a point-and-click approach and directly download the installer by navigating to the installer.zip, the ellipsis option in the upper right corner, and selecting download (or, using the respective keyboard shortcuts once installer.zip has been accessed, e.g., CTRL + SHIFT + S). Downloading expoFitter this way will require your moving the installer from your local downloads to the desired location on your machine before decompressing the file and executing the pseudo-installer pseudo-executable.

expoFitter on shinyapps.io

Lastly, expoFitter has been made publicly available as a web app, which is hosted on shinyapps.io and can be accessed using https://ryellison.shinyapps.io/expofitter/.

Usage

Data Input

• Upload a .csv file using Browse... under Select File containing electrophysiological (e.g., neuronal current) time-series data. Ensure the dataset has at least two columns, e.g.,

where, in this example, \(t\) is time in seconds (s) and \(i\) is current data in nanoamps (nA).

• The backend logic of expoFitter relies on positional encoding of the data (i.e., utilizes data structure indices for lazy data handling). This, however, makes expoFitter more robust in data preparation as column name is inconsequential. All of this is to say, ensure that the dataset is ordered column-wise where the first column contains time data and the second column contains the dynamic process data. If there are more than two columns, column order after the second column is trivial.

Model Selection and Initialization

• The Select Model dropdown menu under Model Initialization allows the user to choose between a ‘Single-Exponential,’ ‘Double-Exponential,’ or the implementation of ‘Both’ models.

• The native model parameter approximator auto-estimates initial conditions based on the data and selected model. The sliders can be used to adjust model parameter (A, B, C, D, etc.) initial values if the auto-estimated parameters fail.

• The Fit Model button must be clicked to run model.

Visualization, Fitting, and Performance Reporting

• expoFitter automatically visualizes the time-series data it ingests.

• Once Fit Model is clicked as described above, expoFitter will utilize the model parameters auto-estimated or manually selected through alteration of the sliders and then fit the model to the dynamic process using non-linear least squares optimization (see Supplemental Information).

• When the model(s) error minimization is complete, the model fit is visualized in the figure.

• The performance report is provided in the Model Solution section, showing the best fit model’s parameters and a quantitative summary of model fitness.

Saving Results

• When data is uploaded to expoFitter the save functionality dynamically appears.

• The user can save the base plot of the electrophysiology data by selecting Save before fitting a model.

• Once a model is fit to the data, the figure observed in the Visualization section can be saved by clicking the Save button in the interface.

All visualizations are saved as a .pdf file.

Supplemental Information

Levenberg-Marquardt Algorithm

Update rule:

\[\mathbf{x}_{k+1} = \mathbf{x}_k - \left( \mathbf{J}^T \mathbf{J} + \lambda \mathbf{I} \right)^{-1} \mathbf{J}^T \mathbf{r}\]

Where:

• \(\mathbf{J}\) is the Jacobian matrix of the residuals,
• \(\mathbf{r}\) is the residual vector (differences between observed and predicted data),
• \(\lambda\) is a damping factor that controls the transition between gradient descent (for stability) and the Gauss-Newton method (for faster convergence).

Gradient Descent (when \(\lambda\) is large)

Update rule:

\[\mathbf{x}_{k+1} = \mathbf{x}_k - \alpha \nabla F(\mathbf{x}_k)\]

Where:

• \(\alpha\) is the learning rate,
• \(\nabla F\) is the gradient of the cost function.

Gauss-Newton Method (when \(\lambda\) is small)

Update rule:

\[\mathbf{x}_{k+1} = \mathbf{x}_k - \left( \mathbf{J}^T \mathbf{J} \right)^{-1} \mathbf{J}^T \mathbf{r}\]

These methods ensure high-fidelity parameter estimation for complex neuroelectrophysiological datasets.